where \(\mu \)  and \(\nu \)  are the ground state shear modulus and Poisson's ratio, respectively, \(I_1\)  is the first principal invariant of the Cauchy-Green strain tensors and \(J\)  expresses the determinant of the deformation gradient. We denote the shear moduli for the film and substrate by \(\mu \)  and \(\mu _{\rm s}\) , respectively, but assume that \(\nu \)  takes the same value for both the film and substrate. A calculation with the aid of Mathematica [1]}, extending the analysis in [2]}, reveals that the compressive strain now has the asymptotic expansion
\(1-\lambda =\frac{2 (\nu -1)^2}{3-4 \nu } \frac{r}{k h} +\frac{1}{12} (kh)^2+d_0 r+d_1 (k h)^4+d_2 r (k h)+d_3 \frac{ r^2}{ (kh)^2}+O((kh)^5),  \) 
